5th root (-3)^5 ._.

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5th root (-3)^5 ._.

Mathematics
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It can be written as the power of a power: \[\large \sqrt[5]{(-3)^{5}}=((-3)^{5})^\frac{1}{5}\]
Just multiply the indices (5 * (1/5).
HI!!

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the fifth root of whatever to the power of five is whatever
\[\huge \sqrt[5]{\diamondsuit^5}=\diamondsuit\]
So if it's the same number it's going to be whatever the inside number is? (I have no clue if that made sense)
@misty1212 Do you think you could help me with another problem?
sure
and yes, it is the same number that is inside, so your answer should be \(-3\)
Cool, um, my next question is a 5th root of -1/32
I don't understand fractions all that well and since I'm new to this whole 5th root, I'm extremely confused about it.
your job is to think of a number that, when raised to the fifth power, is 32
don't think too hard , it is easy to come by that is not the final answer btw, but that is the first step
if you do not get it, let me know if you do, say it
So it'd just be multiplying something by itself to get to 32?
yes one number, multiplied by itself five times, to give 32
i will be happy to tell you if you like
Would it be 2? and since it's a negative 32, the answer would be -2?
yes \(2^5=32\) so \(\sqrt[5]{32}=2\) but as i said, we are still not done
you want \[\sqrt{-\frac{1}{32}}\] which is the same as \[\frac{\sqrt[5] 1}{\sqrt[5]{-32}}\]
\[\sqrt[5]{1}=1\] and \[\sqrt[5]{-32}=-2\]
So would it be the 5th root 1 over -2?
no it would just be \[-\frac{1}{2}\]
not the fifth root, you already took the fifth root
Ohhh, I see now.
ok good !!
Thank you! :)
\[\huge \color\magenta\heartsuit\]

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